Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
In the xy-plane, does the line L intersect the graph of y = x^2
(1) Line L passes through (4, -8)
(2) Line L passes through (-4, 16)
There are 2 variables (slope, y-intercept) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
C actually is the answer, but is too trivial.
If we look at the conditions separately,
condition 1 cannot determine anything
Condition 2 y=x^2 passes through (-4,16) so it's a 'yes' and is sufficient, making the answer (B).
For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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